Operads of compatible structures and weighted partitions

Details Operads of compatible structures and weighted partitions Operads of compatible structures and weighted partitions

2007-06-14

arxiv.org/abs/0706.2196v2

J. Pure Appl. Algebra 212 (2008), no. 11, 2522--2534.

Mathematics

Algebraic Topology

16 pages, main result about Koszulness generalized to a large class of compatible structures

Scientific paper

10.1016/j.jpaa.2008.04.009

In this paper we describe operads encoding two different kinds of compatibility of algebraic structures. We show that there exist decompositions of these in terms of black and white products and we prove that they are Koszul for a large class of algebraic structures by using the poset method of B. Vallette. In particular we show that this is true for the operads of compatible Lie, associative and pre-Lie algebras.

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